1. There is a comment regarding an infant; Torbjørn Olsen. Son of Ole Torbjørnsen Omnes. Probably on board. Yes. The family registration (original doc.) states one infant, yes? In addttion to one child. Can we assume that this reflect who actually borded the ship in Larvik. Was it normal not to register name of infants? If he died on the voyage, any way to find out?
2. Regarding payment. How - and when - was this actually done? A receipt is included in the documents. Both Speciedaler and Dollars are mentioned. Confusing to me.
United States required filing of a passenger list at the 1st port of call in U.S. Sometimes deaths aboard are recorded on the passenger list filed.
If you are searching for a name for the infant, you may want to try the Utflyttede records from Hjartdal or possibly from Larvik, or the baptismal records from Hjartdal and Larvik parishes.
It would seem that payment for the voyage was made in advance. Sometimes, a "local" person is involved in organizing people to go on a voyage and they were responsible for the collection of the payment.
But there are others here who are more familiar with procedures than I.
Since the voyage is prior to 1850 have you looked for the family in the Gerhard Naeseth series The Norwegian Immigrants to the United States: A Biographical Directory 1825-1850 for information about the family?
Personally, I have run into a family who reported a death at their local church which they hadn't memorialized from 6 years before. What do you know about the family in US?